Question

Find the number of ways of distributing n balls in n cells. What will be the number of ways if each cell must be occupied?

Answer 1

For filling first cell, n balls are available.
First cell is filled in n ways.
Second cell is filled in (n – 1) ways
Third cell is filled in (n – 2) ways and so on.
n^th cell is tilled in one way.
Required number
= n (n – 1) (n – 2) … 1
= n!